×

zbMATH — the first resource for mathematics

Nonlinear vibration analysis of an axially moving drillstring system with time dependent axial load and axial velocity in inclined well. (English) Zbl 1385.70042
Summary: In this paper a nonlinear model was developed for a drillstring system in deviated well with axially moving motion and axial loading, using the perturbation techniques.
The drillstring was considered as a simply supported axially moving rotor. Governing equations of motion were obtained based on Hamilton’s principle and method of multiple scales was employed to solve the nonlinear motion equations in order to obtain the steady state response and stability region of the system.
Then the effects of rotating speed, axial compression load, imbalance mass and nonlinear fluid force on the drillstring responses were investigated in detail and nonlinear natural frequencies and their corresponding mode shapes were presented.
Analytical and numerical results reveal the rich and interesting nonlinear phenomena such as primary and parametric resonance that is being investigated for the first time in this study on the nonlinear vibration of the drillstring system.
Finally in effort to validate the theoretical approach employed in this study, the numerical solutions obtained here were compared with a set of existing experimental data.

MSC:
70K99 Nonlinear dynamics in mechanics
70B15 Kinematics of mechanisms and robots
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Mason, J.; Sprawls, B.: Addressing BHA whirl: the culprit in mobile bay, SPE drilling and completion 13, No. 4, 231-236 (1998)
[2] Vandiver, J. K.; Nicholson, J.; Shyu, R. J.: Case studies of the bending vibration and whirling motion of drill collars, SPE drilling engineering 5, No. 4, 282-290 (1990)
[3] Jansen, J.: Non-linear rotor dynamics as applied to oil well drillstring vibrations, Journal of sound and vibration 147, No. 1, 115-135 (1991)
[4] Millheim, K.; Apostal, M.: The effect of bottomhole assembly dynamics on the trajectory of a bit, Journal of petroleum technology 33, No. 12, 2323-2338 (1981)
[5] Mitchell, R.; Allen, M.: Lateral vibration: the key to BHA failure analysis, World oil 200, No. 4, 101-104 (1985)
[6] Chen, S.; Géradin, M.: An improved transfer matrix technique as applied to BHA lateral vibration analysis, Journal of sound and vibration 185, No. 1, 93-106 (1995) · Zbl 1049.74597 · doi:10.1006/jsvi.1994.0365
[7] Vaz, M.; Patel, M.: Analysis of drill strings in vertical and deviated holes using the Galerkin method, Engineering structures 17, No. 6, 437-442 (1995)
[8] M. Dykstra, Nonlinear drill string dynamics, PhD Thesis, University of Tulsa, The Graduate School, 1996.
[9] Dunayevsky, V.; Abbassian, F.; Judzis, A.: Dynamic stability of drillstrings under fluctuating weight on bit, SPE drilling and completion 8, No. 2, 84-92 (1993)
[10] Van Der Heijden, G.: Bifurcation and chaos in drillstring dynamics, Chaos solitons fractals 3, No. 2, 219-247 (1993) · Zbl 0784.58047 · doi:10.1016/0960-0779(93)90068-C
[11] Leine, R. I., Bifurcations in discontinuous mechanical systems of Filippov-type, PhD Thesis, University of Eindhoven, Eindhoven, the Netherlands, 2000.
[12] Theron, A.; De Langre, E.; Putot, C.: The effect of dynamical parameters on precession in rotary drilling, Journal of energy ressource technology 123, 181-186 (2001)
[13] Zamanian, M.; Khadem, S. E.; Ghazavi, M. R.: Stick-slip oscillations of drag bits by considering damping of drilling mud and active damping system, Journal of petroleum science engineering 59, No. 3, 289-299 (2007)
[14] R.J. Shyu, Bending vibration of rotating drill strings, PhD Thesis, Massachusetts Institute of Technology, Department of Ocean Engineering, Cambridge, 1989.
[15] Christoforou, A.; Yigit, A.: Dynamic modeling of rotating drillstrings with borehole interactions, Journal of sound and vibration 206, No. 2, 243-260 (1997)
[16] Tucker, R.; Wang, C.: An integrated model for drill-string dynamics, Journal of sound and vibration 224, No. 1, 123-165 (1999)
[17] Berlioz, A.; Hagopian, J. D.; Dufour, R.; Draoui, E.: Dynamic behavior of a drill string: experimental investigation of lateral instabilities, Journal of vibration and acoustics transactions of the ASME 118, No. 3, 292-298 (1996)
[18] Zifeng, L.; Xingrui, M.; Wenhu, H.; Xisheng, L.: A 3D analysis of a bottomhole assembly under large deflection, SPE drilling and completion 11, No. 2, 104-110 (1996)
[19] Birades, M.: Static and dynamic three-dimensional bottomhole assembly computer models, SPE drilling engineering 3, No. 2, 160-166 (1988)
[20] Khulief, Y. A.; Al-Sulaiman, F. A.; Bashmal, S.: Vibration analysis of drillstrings with self-excited stick-slip oscillations, Journal of sound and vibration 299, 540-558 (2007)
[21] Tikhonov, V. S.; Safronov, A. I.: Investigation of drillstring transverse vibrations at rotary drilling of inclined well, (2002)
[22] Heisig, G.; Neubert, M.: Lateral drillstring vibrations in extended-reach wells, paper IADC/SPE 59235 presented at the IADC/SPE drilling conference, new Orléans, LA, (2000)
[23] Wickert, J. A.; Jr., C. D. Mote: Classical vibration analysis of axially moving continua, Journal of applied mechanics 57, 738-744 (1990) · Zbl 0724.73125 · doi:10.1115/1.2897085
[24] Abrate, S.: Vibrations of belts and belt drives, Mechanical machinery theory 27, No. 6, 645-659 (1992)
[25] Pakdemirli, M.; Ulsoy, A. G.: Stability analysis of an axially accelerating string, Journal of sound and vibration 203, 815-832 (1997)
[26] Wickert, J. A.: Non-linear vibration of a traveling tensioned beam, International journal of non-linear mechanics 27, 503-517 (1992) · Zbl 0779.73025 · doi:10.1016/0020-7462(92)90016-Z
[27] Mockensturm, E. M.; Perkins, N. C.; Ulsoy, A. G.: Stability and limit cycles of parametrically excited, axially moving strings, Journal of vibration and acoustics 118, 346-351 (1996)
[28] Pellicano, F.; Fregolent, A.; Bertuzzi, A.; Vestroni, F.: Primary and parametric non-linear resonances of a power transmission belt: experimental and theoretical analysis, Journal of sound and vibration 244, No. 4, 669-684 (2001)
[29] Chakraborty, G.; Mallik, A. K.; Hatal, H.: Non-linear vibration of traveling beam, International journal of non-linear mechanics 34, 655-670 (1999) · Zbl 1342.74070
[30] Ghayesh, M. H.; Khadem, S. E.: Non-linear vibration and stability analysis of a partially supported conveyor belt by a distributed viscoelastic foundation, Structural engineering and mechanics 27, No. 1, 17-32 (2007)
[31] Ghayesh, M. H.: Nonlinear transversal vibration and stability of an axially moving viscoelastic string supported by a partial viscoelastic guide, Journal of sound and vibration 314, No. 3, 757-774 (2008)
[32] Ghayesh, M. H.; Khadem, S. E.: Rotary inertia and temperature effects on non-linear vibration, steady-state response and stability of an axially moving beam with time-dependent velocity, International journal of mechanical science 50, No. 3, 389-404 (2008) · Zbl 1264.74088
[33] Oz, H. R.: On the vibration of an axially traveling beam on fixed supports with variable velocity, Journal of sound and vibration 239, 556-564 (2001)
[34] Marynowski, K.; Kapitaniak, T.: Zener internal damping in modeling of axially moving viscoelastic beam with time-dependent tension, International journal of non-linear mechanics 42, No. 1, 118-131 (2007) · Zbl 1200.74076 · doi:10.1016/j.ijnonlinmec.2006.09.006
[35] Dufour, R.; Berlioz, A.: Parametric instability of a beam due to axial excitations and to boundary conditions, ASME journal of vibration and acoustics 120, 461-467 (1998)
[36] Christoforou, A. P.; Yigit, A. S.: Fully coupled vibrations of actively controlled drillstrings, Journal of sound and vibration 267, 1029-1045 (2003)
[37] Jansen, J. D.; Den Steen, L. Van; Zachariasen, E.: Active damping of torsional drillstring vibrations with a hydraulic top drive, SPE drilling and completion 10, 250-254 (1995)
[38] Meirovitch, L.: Analytical methods in vibrations, (1967) · Zbl 0166.43803
[39] Washizu, K.: Variational methods in elasticity and plasticity, (1982) · Zbl 0498.73014
[40] Harris, C. M.; Piersol, A. G.: Harris shock and vibration handbook, (2002)
[41] Nayfeh, A. H.; Mook, D. T.: Nonlinear oscillations, (1979) · Zbl 0418.70001
[42] Nayfeh, A. H.; Nayfeh, J. F.; Mook, D. T.: On methods for continuous systems with quadratic and cubic nonlinearities, Nonlinear dynamics 3, 145-162 (1992)
[43] Dareing, D.; Livesay, B.: Longitudinal and angular drill-string vibrations with damping, Journal of energy resources technology transactions of the ASME 90, No. 4, 671-679 (1968)
[44] A. Sengupta, Dynamic modeling of roller cone bit lift-off in rotary drilling, Master’s Thesis, Rice University, Department of Mechanical Engineering, Houston, Texas, 1993.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.